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I think a lot of topics are much less sequential the further you go. As an adult I spend most of my time repeating the fundamentals of my field, and learning a

I think a lot of topics are much less sequential the further you go. As an adult I spend most of my time repeating the fundamentals of my field, and learning a topic deeply as needed. For children it probably makes sense to cram the multiplication tables.

Nevermark 2y ago
I would think that the opportunities to immediately "use" multiplication, instead of just practice it for tests, or some future numerate citizenship, would be omnipresent. If you don't use something after you learned it, you miss out on: 1. Learning how it is actually applied 2. Discovering how the knowledge is useful for you personally, in ways you may not expect if you don't actually experience using it 3. Deeper understanding and mastery of the knowledge 4. Much much much better retention It is worth creating some immediate use for new knowledge, even the smallest possible useful or creative project, for better retention alone. > learning a topic deeply as needed That is the ultimate use-driven learning model. As for non-sequential, I agree. The more we manage our own learning, the more it is a directed graph (i.e. prerequisites translate to many follow up paths), and eventually just graphs (many ways to order topics, and alternate combinations of prerequisites for each topic, in any complex area).
- zeroCalories 2y ago
  To be clear, in the context of this article, the alternative to drilling multiplication until you've memorized it is to space out the learning over a period of time. It's probably good to study for the test, because next week we're learning PEMDAS, so you better be solid on your multiplication.
formerly_proven 2y ago
Basically all undergrad stuff is fundamentals and "optimized cramming" (we call it bulimic learning, because you stuff knowledge into you just in time to throw it back up in the test) means tons of people "achieve" degrees without being even dimly aware of the existence of the fundamentals afterwards. If you have a bachelor's degree in e.g. computer science, the idea of encoding data shouldn't be an unknown unknown to you.
shortrounddev2 2y ago
They don't teach multiplication tables anymore as far as I know. I didn't learn them and I was born in 1995
- Brybry 2y ago
  Wouldn't that be weird given that it's part of common core? > By the end of Grade 3, know from memory all products of two one-digit numbers. [1] https://www.thecorestandards.org/Math/Content/3/OA/#CCSS.Math.Content.3.OA.C.7 https://www.thecorestandards.org/Math/Content/3/OA/#CCSS.Mat...
  - lupire 2y ago
    Knowing the products is not the same as using or cramming the tables. It is quite sufficient (and probably superior) to learn the facts through use, for that makes them robust.
  - shortrounddev2 2y ago
    I learned that through brute force. They just had us multiply numbers over and over again rather than memorizing the table
- Tempest1981 2y ago
  Interesting, in the US? What state?
  - shortrounddev2 2y ago
    Virginia
- gumby 2y ago
  They still teach them in Germany, though I think maybe only up to 10x10 these days. In the US AFAIK they are called "times tables"; in Germany "one times one" („Einmaleins‟). It's funny what people emphasize for the same thing.
  - 2y ago

Nevermark 2y ago

I would think that the opportunities to immediately "use" multiplication, instead of just practice it for tests, or some future numerate citizenship, would be omnipresent. If you don't use something after you learned it, you miss out on: 1. Learning how it is actually applied 2. Discovering how the knowledge is useful for you personally, in ways you may not expect if you don't actually experience using it 3. Deeper understanding and mastery of the knowledge 4. Much much much better retention It is worth creating some immediate use for new knowledge, even the smallest possible useful or creative project, for better retention alone. > learning a topic deeply as needed That is the ultimate use-driven learning model. As for non-sequential, I agree. The more we manage our own learning, the more it is a directed graph (i.e. prerequisites translate to many follow up paths), and eventually just graphs (many ways to order topics, and alternate combinations of prerequisites for each topic, in any complex area).

zeroCalories 2y ago
To be clear, in the context of this article, the alternative to drilling multiplication until you've memorized it is to space out the learning over a period of time. It's probably good to study for the test, because next week we're learning PEMDAS, so you better be solid on your multiplication.

formerly_proven 2y ago

Basically all undergrad stuff is fundamentals and "optimized cramming" (we call it bulimic learning, because you stuff knowledge into you just in time to throw it back up in the test) means tons of people "achieve" degrees without being even dimly aware of the existence of the fundamentals afterwards. If you have a bachelor's degree in e.g. computer science, the idea of encoding data shouldn't be an unknown unknown to you.

shortrounddev2 2y ago

They don't teach multiplication tables anymore as far as I know. I didn't learn them and I was born in 1995

Brybry 2y ago
Wouldn't that be weird given that it's part of common core? > By the end of Grade 3, know from memory all products of two one-digit numbers. [1] https://www.thecorestandards.org/Math/Content/3/OA/#CCSS.Math.Content.3.OA.C.7 https://www.thecorestandards.org/Math/Content/3/OA/#CCSS.Mat...
- lupire 2y ago
  Knowing the products is not the same as using or cramming the tables. It is quite sufficient (and probably superior) to learn the facts through use, for that makes them robust.
- shortrounddev2 2y ago
  I learned that through brute force. They just had us multiply numbers over and over again rather than memorizing the table
Tempest1981 2y ago
Interesting, in the US? What state?
- shortrounddev2 2y ago
  Virginia
gumby 2y ago
They still teach them in Germany, though I think maybe only up to 10x10 these days. In the US AFAIK they are called "times tables"; in Germany "one times one" („Einmaleins‟). It's funny what people emphasize for the same thing.
- 2y ago